Quantum Information Self-Organization and Consciousness: a Holoinformational Model of Consciousness

Abstract. The author proposes a holoinformational view of consciousness based on the holonomic theory of brain function and quantum brain dynamics developed by Karl Pribram, Sir John Eccles, Hameroff, Jibu and Yasue, and on the quantum-holographic and holomovement theory of David Bohm. This conceptual framework is integrated into the non-local information property of the Quantum Field Theory of Umesawa, to the concept of negentropy, order, and organization developed by Shannon, Wiener, Szilard and Brillouin, and to the theories of self-organization and complexity of Prigogine, Atlan, Jantsch and Kauffman. Wheeler’s “it from bit” concept of a participatory universe, and the developments of the physics of information made by Zurek and others with the concepts of statistical entropy and algorithmic entropy, related to the number of bits being processed in the mind of the observer, are also considered. This new synthesis gives a self-organizing quantum non-local informational basis for a new model of consciousness in a participatory universe. In this synthesis, consciousness is conceived as a meaningful quantum non-local information interconnecting the brain and the cosmos, by a holoinformational field (a field at the same time non-local holistic (quantum) and local (Newtonian). We propose that we are this very non-local quantum-holographic cosmos that manifests itself through our consciousness, interconnecting in a participatory holistic and indivisible way the human brain to all levels of the self-organizing holographic multiverse

Entropy and Quantum Kolmogorov Complexity: A Quantum Brudno's Theorem

In classical information theory, entropy rate and Kolmogorov complexity per symbol are related by a theorem of Brudno. In this paper, we prove a quantum version of this theorem, connecting the von Neumann entropy rate and two notions of quantum Kolmogorov complexity, both based on the shortest qubit descriptions of qubit strings that, run by a universal quantum Turing machine, reproduce them as outputs.Comment: 26 pages, no figures. Reference to publication added: published in the Communications in Mathematical Physics (http://www.springerlink.com/content/1432-0916/

Quantum Kolmogorov Complexity and Quantum Key Distribution

We discuss the Bennett-Brassard 1984 (BB84) quantum key distribution protocol in the light of quantum algorithmic information. While Shannon's information theory needs a probability to define a notion of information, algorithmic information theory does not need it and can assign a notion of information to an individual object. The program length necessary to describe an object, Kolmogorov complexity, plays the most fundamental role in the theory. In the context of algorithmic information theory, we formulate a security criterion for the quantum key distribution by using the quantum Kolmogorov complexity that was recently defined by Vit\'anyi. We show that a simple BB84 protocol indeed distribute a binary sequence between Alice and Bob that looks almost random for Eve with a probability exponentially close to 1.Comment: typos correcte